Numeric.Log:$clog1p from log-domain-0.10.2.1, B

Average Error: 0.2 → 0.2

Time: 8.0s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{x}{1 + \sqrt{x + 1}}\]

↓

\[\frac{x}{1 + \sqrt{x + 1}}\]

C

double f(double x) {
        double r144524 = x;
        double r144525 = 1.0;
        double r144526 = r144524 + r144525;
        double r144527 = sqrt(r144526);
        double r144528 = r144525 + r144527;
        double r144529 = r144524 / r144528;
        return r144529;
}

↓

double f(double x) {
        double r144530 = x;
        double r144531 = 1.0;
        double r144532 = r144530 + r144531;
        double r144533 = sqrt(r144532);
        double r144534 = r144531 + r144533;
        double r144535 = r144530 / r144534;
        return r144535;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

   \[\frac{x}{1 + \sqrt{x + 1}}\]

2. Final simplification 0.2

   \[\leadsto \frac{x}{1 + \sqrt{x + 1}}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))